Why won't Blender run on Windows XP?
The last version of blender that was officially compatible with Windows XP was blender 2.76. Versions after that probably won't work. You can download previous version of blender here.

To quote Martijn Berger (a blender developer) from here on why support for XP was dropped:


  We implicitly dropped Windows XP when switching to python 3.5. Python
  has the so called PEP system and PEP 11 "Removing support for little
  used platforms" defines the support for windows XP to be over at the
  same time Microsoft stopped supporting it. Since python 3.5 released
  after XP died it does not support XP.
  
  While it might be possible to backport python 3.5 to windows XP i
  think that we should not do this.
  
  So blender 2.77 will not run on XP. The 32 bit release requires Vista
  or newer and the 64 bit release Windows 7 SP1 or newer.